Kirlin R.L., Done W.J. (eds.) Covariance Analysis for Seismic Signal Processing

Society of Exploration Geophysicists, 1999. — 355 p.This volume is intended to give the geophysical signal analyst sufficient material to understand the usefulness of data covariance matrix analysis in the processing of geophysical signals. A background of basic linear algebra, statistics, and fundamental random signal analysis is assumed. This reference is unique in that the data vector covariance matrix is used throughout. Rather than dealing with only one seismic data processing problem and presenting several methods, the concentration in this book is on only one fundamental methodology - analysis of the sample covariance matrix presenting many seismic data problems to which the methodology applies. This volume should be of interest to many researchers, providing a method amenable to many distinct applications. It offers a diverse sampling and discussion of the theory and the literature developed to date from a common viewpoint.Data Vectors and Covariance Matrices
Eigenstructure, the Karhunen Loeve Transform, and Singular-Value Decomposition
Vector Subspaces
Temporal and Spatial Spectral Analysis
Root-Mean-Square Velocity Estimation
Subspace-Based Seismic Velocity Analysis
Enhanced Covariance Estimation with Application to the Velocity Spectrum
Waveform Reconstruction and Elimination of Multiples and Other Interferences
Removal of Interference Patterns in Seismic Gathers
Principal Component Methods for Suppressing Noise and Detecting Subtle Reflection Character Variations
Eigenimage Processing of Seismic Sections
Single-Station Triaxial Data Analysis
Correlation Using Triaxial Data from Multiple Stations in the Presence of Coherent Noise
Parameterization of Narrowband Rayleigh and Love Waves Arriving at a Triaxial Array